Optimal Leader/Mentor Matching

Source: R/mentor.r

Implementes the algorithm described in Valente and Davis (1999)

mentor_matching(
  graph,
  n,
  cmode = "indegree",
  lead.ties.method = "average",
  geodist.args = list()
)

leader_matching(
  graph,
  n,
  cmode = "indegree",
  lead.ties.method = "average",
  geodist.args = list()
)

# S3 method for class 'diffnet_mentor'
plot(
  x,
  y = NULL,
  vertex.size = "degree",
  minmax.relative.size = getOption("diffnet.minmax.relative.size", c(0.01, 0.04)),
  lead.cols = grDevices::topo.colors(attr(x, "nleaders")),
  vshapes = c(Leader = "square", Follower = "circle"),
  add.legend = TRUE,
  main = "Mentoring Network",
  ...
)

Arguments

graph

Any class of accepted graph format (see netdiffuseR-graphs).

n

Number of leaders

cmode

Passed to dgr.

lead.ties.method

Passed to rank

geodist.args

Passed to approx_geodesic.

x

An object of class diffnet_mentor.

y

Ignored.

vertex.size

Either a numeric scalar or vector of size \(n\), or any of the following values: "indegree", "degree", or "outdegree" (see details).

minmax.relative.size

Passed to rescale_vertex_igraph.

lead.cols

Character vector of length attr(x,"nleaders"). Colors to be applied to each group. (see details)

vshapes

Character scalar of length 2. Shapes to identify leaders (mentors) and followers respectively.

add.legend

Logical scalar. When TRUE generates a legend to distinguish between leaders and followers.

main

Character scalar. Passed to title

...

Further arguments passed to plot.igraph

Value

An object of class diffnet_mentor and data.frame with the following columns:

name

Character. Labels of the vertices

degree

Numeric. Degree of each vertex in the graph

iselader

Logical. TRUE when the vertex was picked as a leader.

match

Character. The corresponding matched leader.

The object also contains the following attributes:

nleaders

Integer scalar. The resulting number of leaders (could be greater than n)

.

graph

The original graph used to run the algorithm.

Details

The algorithm works as follows:

  1. Find the top n individuals ranking them by dgr(graph, cmode). The rank is computed by the function rank. Denote this set M.

  2. Compute the geodesic matrix.

  3. For each v in V do:

    1. Find the mentor m in M such that is closest to v

    2. Were there a tie, choose the mentor that minimizes the average path length from v's direct neighbors to m.

    3. If there are no paths to any member of M, or all have the same average path length to v's neighbors, then assign one randomly.

Plotting is done via the function plot.igraph.

When vertex.size is either of "degree", "indegree", or "outdegree", vertex.size will be replace with dgr(.,cmode = ) so that the vertex size reflects the desired degree.

The argument minmax.relative.size is passed to rescale_vertex_igraph which adjusts vertex.size so that the largest and smallest vertices have a relative size of minmax.relative.size[2] and minmax.relative.size[1] respectively with respect to the x-axis.

References

Valente, T. W., & Davis, R. L. (1999). Accelerating the Diffusion of Innovations Using Opinion Leaders. The ANNALS of the American Academy of Political and Social Science, 566(1), 55–67. doi:10.1177/000271629956600105

Examples

# A simple example ----------------------------------------------------------
set.seed(1231)
graph <- rgraph_ws(n=50, k = 4, p = .5)

# Looking for 3 mentors
ans <- mentor_matching(graph, n = 3)

head(ans)
#>   name degree isleader match
#> 1    1      4    FALSE    49
#> 2    2      2    FALSE    17
#> 3    3      2    FALSE    22
#> 4    4      3    FALSE    20
#> 5    5      3    FALSE     6
#> 6    6      6     TRUE     6
table(ans$match) # We actually got 9 b/c of ties
#> 
#> 15 17 20 22 33 43 49  6  9 
#>  7  5  2  5  5  3  8 12  3 

# Visualizing the mentor network
plot(ans)